When optical signals are transmitted over optical links, different wavelength components of the optical signals will generally experience different propagation times due to the fact that the transport medium (such as an optical fiber) has different effective refractive indices for different wavelengths. This phenomenon is referred to as dispersion, or chromatic dispersion. One effect of dispersion is that an optical pulse, which always has some finite width in wavelength, will be broadened, since different wavelength components of the pulse will travel at slightly different group velocities through the optical link. Such broadening of optical pulses caused by the dispersion may lead to a situation at the receiver end where it is difficult to separate adjacent pulses from each other during detection. Particularly for high modulation rate systems, dispersion becomes a severely limiting factor. For this reason, it is typically required to use some kind of dispersion compensation along the optical link and/or at the receiver side.
The group velocity vg, i.e. the velocity at which amplitude modulations (signals) travel in a material, is given by
                              v          g                =                  c                                    n              ⁡                              (                λ                )                                      -                          λ              ⁢                                                ⅆ                  n                                                  ⅆ                                                                          ⁢                  λ                                                                                        (        1        )            where c is the speed of light in vacuum, n is the wavelength-dependent effective index, and λ is the vacuum wavelength. The denominator of this expression is known as the group index ng. The propagation time τ for a signal over a length L can then be written as τ=L·(ng/c). The dispersion is defined as the rate of change of the group propagation time τ with respect to wavelength λ, normalized to the propagation length L. Hence, using equation (1) above, the dispersion D is given by:
                    D        =                                            1              L                        ·                                          ⅆ                τ                                            ⅆ                                                                  ⁢                λ                                              =                                    -                              λ                c                                      ·                                                                                ⅆ                    2                                    ⁢                  n                                                  ⅆ                                                                          ⁢                                      λ                    2                                                              ⁢                                                          [                              ps                ·                                                      (                                          km                      ·                      nm                                        )                                                        -                    1                                                              ]                                                          (        2        )            
If the dispersion is positive, then the high frequency part (short wavelength) of an optical signal will arrive earlier at the receiver side compared to the low frequency part.
As can be seen from the expression (2) above, the dispersion varies with the wavelength range. Optical fibers typically have a wavelength at which the dispersion is zero, called the zero dispersion wavelength, which means that two wavelength channels close to such wavelength have a comparatively small difference in group velocities. For two other wavelength channels, having the same spectral spacing as before but located further away from the zero dispersion wavelength, there will be a considerably larger difference in group velocities. For a typical silica optical fiber used for optical links, the zero dispersion wavelength appears close to 1300 nm. However, attenuation at this wavelength is quite high, and for long-haul communications it is desirable to operate around 1550 nm, where attenuation is considerably lower, but on the other hand dispersion is considerably higher. The zero dispersion wavelength can be shifted by adding dopants to the fiber and/or by altering the core diameter of the fiber, but this introduces other problems.
The dispersion slope in an optical fiber can, for any given wavelength range, be positive or negative. Positive dispersion slope means that the dispersion increases with increasing wavelength, while negative dispersion slope means that the dispersion decreases with increased wavelength.
It is a general desire to keep the total dispersion effects of any optical communications link to a minimum. For example, this could be achieved by combining positive and negative dispersion in the link. If the transport fiber has positive dispersion for the wavelength range at issue, compensation could be effected by passing the optical signal through an additional piece of fiber having negative dispersion, wherein the length and dispersion of the compensating fiber are selected to balance the dispersion effects of the transport fiber. In order to compensate for dispersion in many wavelength channels simultaneously, the dispersion slope of the compensating fiber must also be balanced to the dispersion slope of the transport fiber. An apparent drawback of this approach, however, is that very long compensating fibers are needed, which causes additional problems relating to insertion loss, second order effects, etc.
In order to reduce the required length of the compensating optical fiber, it has previously been proposed to use fiber Bragg gratings in a dispersion compensation module.
One example of a dispersion compensation module (DCM) according to the prior art comprises a long (˜10 m), chirped fiber Bragg grating, in which the low frequency part (long wavelengths) of the optical signal is reflected close to the input end of the grating and the high frequency part (short wavelengths) is reflected closer to the opposite end of the grating. The additional propagation path that the high frequency part has to travel across the grating compensates for the difference in propagation time between the low and high frequency parts caused by dispersion in the optical link. For compensation of a standard SMF-28 fiber link over the entire C band, such grating must typically be about 5-10 m long. However, due to the high requirements on the fiber Bragg grating, it becomes very difficult to manufacture such long gratings.
Another approach for making a dispersion compensation module is to use a so-called channelized device, wherein the dispersion is compensated only around the actual channels used in the WDM signal, and not in between the channels. The channels are specified by the ITU grid (International Telecommunication Union) for each of the S-, C-, and L-band. By compensating dispersion only for wavelengths where there might actually be a signal present, the requirement of the grating length can be relaxed considerably. For example, with proper design, the total length of the grating for compensating all channels in the C-band can be reduced to about 0.1-0.2 m for a channelized device.
One straight-forward way of making a grating-based channelized dispersion compensation module is to simply superimpose gratings for all individual channels in the same length of fiber. In theory, this approach is based on the fact that all gratings are spectrally independent, and the optical radiation will interact only with the proper one of all the superimposed gratings. However, when a large number of gratings are superimposed, the available modulation depth for the refractive index in the optical fiber will become saturated. It can be shown that, for N superimposed gratings of equidistant Bragg frequencies, the modulation envelop for all gratings will take a form that resembles a pulse train—the modulation envelop takes on large values in narrow, regularly spaced regions along the grating and zero in between, wherein the peak amplitude for the envelop is N times the peak amplitude for a single grating. For any practical device, the number of gratings that can be superimposed in the same length of optical fiber is therefore limited, because saturation of the refractive index modulation eventually leads to a situation where the refractive index becomes more or less constant along the fiber. In other words, since the available modulation depth in the fiber is limited, refractive index changes will eventually be induced “everywhere” in the fiber up to the available modulation depth (i.e. the modulation becomes severely saturated).
A channelized grating can also be implemented by making a so-called sampled grating. The final grating profile is similar to the overall envelop obtained by superimposing individual gratings according to above, but the sampled grating is obtained by directly determining the grating amplitude rather than by gradually building up the profile by superimposing sub-gratings. It is well known from Fourier mathematics that a periodic modulation of any function creates equidistant side-bands in the spectral domain, where the spectral separation of the side-bands is inversely proportional to the spatial modulation period. Thus, the reflected channels in a sampled grating can be regarded as side-bands induced by the periodic modulation of a fundamental grating. However, also this latter method is limited by the available refractive index modulation depth of optical fibers.
Hence, both for the method of superimposing individual gratings and for the method of sampling a grating to create side-bands, saturation of the photosensitivity in the optical fiber during the process of writing the gratings will limit the available modulation depth. The maximum amplitude that can be obtained in a channelized, superimposed grating is thus a factor N lower than in a continuous dispersion compensating grating. Thereby, the reflection of the grating decreases and the insertion loss of the device increases accordingly. Nonlinear response in the photosensitive fiber may introduce additional degradation.
All prior art approaches according to the above are associated with various drawbacks. For this reason, attempts have been made to devise other types of channelized gratings for dispersion compensation. Spectral side-bands to a function can be created not only by means of a periodic amplitude modulation, but also by means of a periodic phase modulation, or by a combination of the two.
U.S. Pat. No. 6,707,967 discloses a channelized grating created by a phase sampling modulation scheme. Each period of the sampled grating is divided into a number of sub-intervals. In each of these sub-intervals, the phase takes on a constant value, and the phase φ is restricted to a finite set of Ns allowed values, where φε{2πk/Ns, k=0, 1, . . . , Ns−1}. The final design parameters are selected by applying a Simulated Annealing algorithm, which optimizes the performance of the device in the available phase space. It turns out that the phase modulation scheme is more efficient than the amplitude modulation scheme, in the sense that the ratio between the maximum amplitude in the N-channel grating and in a corresponding single-channel grating is much smaller than N. This is due to the fact that the amplitude is non-zero everywhere in the grating, in contrast to the amplitude modulation scheme, and that all parts of the grating therefore take part in the interaction with the incoming optical radiation, at least for some frequencies.
However, the phase sampling technique according to U.S. Pat. No. 6,707,967 has some limitations. Since the available phase space is discrete and since the Simulated Annealing algorithm has a finite conversion rate, the overall optimum will not be reached. At best, a local optimum will be obtained. Figure of merits in terms of group-delay ripple, insertion loss variation inside an ITU-grid point window, insertion loss variation between the ITU-grid point windows, spectral width around each ITU-grid point etc. are therefore suboptimal. Moreover, this technique leads to problems when implementing the required, discrete phase jumps, particularly when using phase masks. Even with a perfect phase mask, there will be introduced aberrations due to the distance between the fiber core and the phase mask during fabrication of the gratings.